A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications

The system of partial differential equations -div (vDu) = f in Q vertical bar Du vertical bar - 1 = 0 in {v > 0} arises in the analysis of mathematical models for sandpile growth and in the context of the Monge-Kantorovich optimal mass transport theory. A representation formula for the solutions of a related boundary value problem is here obtained, extending the previous two-dimensional result of the first two authors to arbitrary space dimension. An application to the minimization of integral functionals of the form integral(Omega) [h(vertical bar Du vertical bar)-f(x)u]dx, with f >= 0, and h >= 0 possibly non-convex, is also included

A Boundary Value Problem for a PDE Model in Mass Transfer Theory: Representation of Solutions and Applications

Abstract The system of partial differential equations arises in the analysis of mathematical models for sandpile growth and in the context of the Monge-Kantorovich optimal mass transport theory. A representation formula for the solutions of a related boundary value problem is here obtained, extending the previous two-dimensional result of the first two authors to arbitrary space dimension. An application to the minimization of integral functionals of the form with f ≥ 0, and h ≥ 0 possibly non-convex, is also included